Convection Parameters

Jurgen Grieser

June 26, 2012

1 Introduction

There are many parameters used for the identification of weather situations whichare likely to produce thunderstorms with severe weather. They all follow simplifiedconceptual models of the conditions that cause convection. Thresholds have been definedfor most of the parameters to transform them to different levels of warnings. However,false alarm rates are generally high and probability of detection can be low.

2 Parameters

Here is a commented list of some convection parameters. The author is pretty surethat though most of the widely used parameters are included, many may not. The listonly reflects my current knowledge. Most of the parameters are based on a single aspectlinked to convection. However, some of the more modern ones combine those parametersvery successfully. I group them into 5 groups, starting with the simplest temperature-only based indices, those which include humidity and then those related to wind. Thefourth and the fifth group contain some advanced parameters and finally thematic onesrelated to specific perils like hail, downdrafts and lightening.

2.1 Simple temperature-based Indices

1. Lapse Rate - γγ (the negative vertical temperature gradient−dT

dz ) provides information about thestability of an atmospheric layer. An ascending air parcel with a cooling rate lowerthan γ eventually becomes warmer than its environment and accelerates. Thefaster the temperature decreases with height the more unstable is the atmosphere.The following stability criteria apply:

γ ≥ 9.8◦Ckm : absolute unstable atmosphere

γ = 9.8◦Ckm : dry adiabatic lapse rate

9.8◦Ckm > γ ≤ 6

◦Ckm : conditionally unstable

6◦Ckm ≥ γ ≥ 5.5

◦Ckm : moist adiabatic

5.5◦Ckm > γ : stable.

(1)

In case of conditional instability, values of CAPE can become positive and values

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of LI can become negative, meaning that thunderstorms can develop. Unstableconditions cannot last for long.

Sometimes the largest cooling rate of an atmospheric column is used to evaluateits stability. Furthermore the lapse rate of the lowest 500m above ground γ0−500

is used to estimate the stability of the boundary layer. A threshold of 10 to 11K/km characterizes unstable conditions in this case. However, the surface airtemperature is a very uncertain variable in models and so values of γ0−500 canbecome very unrealistic. Another variable is the lapse rate directly above theboundary layer, i.e. γ2000−4000m. A temperature decrease of 8K/km is assumed tobe a threshold separating stable and unstable conditions.

2. Vertical Totals - V TThe vertical totals index (see Miller, 1972) is the temperature difference betweenthe 850hPa level and the 500hPa level

V T = T850 − T500. (2)

It is therefore a measure of the average vertical temperature gradient of a layer ofthe atmosphere starting approximately at the top of the atmospheric boundarylayer and extending through half of the air mass. The stronger the vertical tem-perature gradient the more likely are thunderstorms. Usually a threshold of 26K isassumed to best separate thunderstorm prone weather from weather that cannotproduce thunderstorms. V T = 26K equals approximately a vertical temperaturegradient of 0.65K/100m, i.e. the average observed lapse rate.

3. Boyden Index - BoydIThe Boyden Index (Boyden, 1963) was originally designed to assess the thunder-storm risk at frontal passages. Explicitly it takes only the temperature in 700 hPainto account. However, the height difference of the 1000 and 700 hPa level, i.e. thethickness of this layer is proportional to its mean temperature as well. The indexis defined as

BoydI = 0.1(z700 − z1000)− T700.− 200 (3)

and should not be used outside frontal passages e.g. for air mass thunderstorms.

4. CAPCAP is a stable region in the lower troposphere that impedes convection from theboundary layer. The formal definition is the maximum temperature difference of alifted parcel and its environment. CAP exists mainly in morning soundings duringsummer season. CAP can only be used to tell something about the resistanceagainst convection of low level air parcels. It is related to CIN . The followingthresholds apply:

CAP ≤ 0K : no CAP0K < CAP ≤ 2K : weak CAP2K < CAP ≤ 4K : moderate CAP

4K < CAP : strong CAP.

(4)

If there is a weak CAP and sufficient CAPE storms are likely to occur soon.If there is a strong CAP strong forcing is necessary to overcome it and startconvection even if there is sufficient CAPE.

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2.2 Temperature and Humidity based Indices

1. Cross Totals - CTThe cross totals index (Miller, 1972) overcomes the disadvantage of VT not toinclude humidity. Thunderstorms cannot develop if there is not enough humidityeven in case of strong vertical temperature gradients. Thus, the cross totals in-dex is defined as the difference of the dew-point temperature in 850hPa and thetemperature in 500hPa

CT = Td,850 − T500. (5)

It therefore increases with increasing humidity in lower levels of the atmosphere.The chance for thunderstorms to occur increases if CT is above 20K and heavyshowers and tornadoes are supposed to be likely if CT is above 29K.

2. Total Totals TTThe totals totals index (Miller, 1972) is the sum of V T and CT . It thereforeincreases with increasing humidity in the lower levels of the atmosphere and in-creasing vertical temperature gradients

TT = V T + CT = T850 − T500 + Td,850 − T500 = T850 + Td,850 − 2T500. (6)

The following three thresholds are usually applied:

TT

≥ 44K thunderstorms possible≥ 50K severe thunderstorms possible≥ 55K severe thunderstorms likely.

(7)

3. Modified Total Totals - TTmThe modified TT uses the average of the surface (2m), the 925hPa and the 850hPaobservations instead of the 850hPa observations alone in order to better describethe state of the boundary layer.

TTm = (T2m + T925 + T850)/3 + (Td,2m + Td,925 + Td,850)/3− 2T500. (8)

The threshold for thunderstorms to occur is usually set to 57K.

4. K Index - KThe K index is developed by George (1960). Like the V T it is based on the verticaltemperature gradient between 850hPa and 500hPa. Higher humidity in 850hPa,expressed by higher Td,850 increases K. Furthermore, lower humidity in higherlevels, expressed by the dew-point depression in 700hPa decreases the chance ofthunderstorms to occur resulting in

K = T850 − T500 + Td,850 − (T700 − Td,700). (9)

When all temperatures are provided in ◦C the following thresholds are usuallyapplied:

K

0K to 20K 0% to 20% thunderstorm probability21K to 25K 20% to 40% thunderstorm probability26K to 30K 40% to 60% thunderstorm probability31K to 35K 60% to 80% thunderstorm probability36K to 40K 80% to 90% thunderstorm probability

> 40K 90% to nearly 100% thunderstorm probability.

(10)

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5. Modified K Index - Kmod

As an improvement of the K index the 850hPa temperatures are replaced by theln p weighted temperatures of the surface (2m) and 850hPa by Charba (1977)

K = T − T500 + Td − (T700 − Td,700). (11)

This should be an improvement since now the K index contains also informationof the layer below 850hPa.

6. Humidity Index HIIt is defined by Litynska et al. (1976) closely to the K index as

HI = (T850 − Td,850) + (T700 − Td,700) + (T500 − Td,500) (12)

A value of 30K is suggested as a threshold for thunderstorms with thunderstormsmore likely for smaller values.

7. S Index - SISI uses the same variables as K but in different proportions. It is defined as

SI = TT − (T700 − Td,700)−

0 if V T > 252 if 25 ≥ V T ≥ 226 if 22 > V T.

(13)

SI is introduced by the German Military Geophysical Office (Reymann et al.,1998) and is considered useful from April to September. It is very similar to theK index. In fact it can also be written as K − T500 − ζ where ζ is the third termon the right hand side of eq. (13) which penalizes in case of low values of V T , i.e.low vertical temperature gradients.

8. Rackliff Index - RaIRaI compares the potential wet bulb temperature at 900hPa to the dry bulbpotential temperature at 500hPa

RaI = Θw,900 −Θ500. (14)

Therefore it provides information about the latent instability of an air mass at900hPa, a non-standard height.

9. Modified Jefferson Index JEFFAs the K also JEFF (Jefferson, 1963a,b, 1966) uses the dew-point temperatureat 850hPa and the dew-point depression at 700hPa. However, instead of thetemperature difference between the 850hPa and the 500hPa level it uses thepotential wet-bulb temperature at 850hPa

JEFF = 1.6Θw,850 + Td,850 −−0.5(T700 − Td,700)− 8. (15)

This Index is a further development of the Rackliff Index. It uses standard alti-tudes and is less temperature sensitive. This index is usually applied to air massthunderstorms without any dynamical trigger. A usual threshold for JEFF is29◦C. In polar air masses a somewhat smaller threshold of 27◦C applies.

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10. Adedokun Index - AIAI (defined by Adedokun, 1981, 1982) is the difference of wet bulb temperature at850hPa (or alternatively 2m) and the saturated wet bulb temperature at 500hPa

AI = Θw,850 −Θws,500. (16)

11. Bradbury Index - BradIThis index defined by Bradbury (1977) is also called Potential Wet-Bulb Indexsince it assesses potential instability by wet-bulb temperatures

BradI = Θw,500 −Θw,850. (17)

This index is also called Pickup Index after Pickup (1982). The lower the indexthe stronger is potential instability. This is why this index is sometimes calledpotential instability index, which should not be confused with the PII introducedby Van Delden (2001). A threshold of -2K in summer and 3K in other seasons issometimes suggested.

12. Potential Instability Index - PIIThis index is defined by Van Delden (2001) and measures potential instability ofthe atmospheric layer between 925 and 500hPa

PII =Θe,925 −Θe,500.

z500 − z950(18)

PII is a discretized version of the more generic Convective Potential.

13. Ko Index - KoKo (Andersson et al., 1989) describes the potential instability between lower andhigher levels of the atmosphere. It is thus based on the equivalent potential tem-peratures Θe as

Ko = 0.5(Θe,500 + Θe,700)− 0.5(Θe,850 + Θe,1000). (19)

It is smallest if dry and cold air lies above warm and humid air. Usual thresholdsare

Ko > 5K no thunderstorms possible5K ≥ Ko > 3K thunderstorms possible

2K ≥ Ko severe thunderstorms possible.(20)

14. Convective Instability Index - CICI is an estimate of potential instability of the lower to medium tropospherebased on Θe. It compares Θe of the surface and near-surface layer to the one in500hPa

CI = 0.5 ∗ (Θe,2m + Θe,925)−Θe,500. (21)

A usual threshold is 5◦.

15. Lifted Index - LILI is a measure of stability of the atmosphere between z = 0 and 500hPa. Definedby Galway (1956) it is the temperature difference of a parcel that is lifted from thesurface to its LCL dry adiabatically and further pseudo adiabatically to 500hPa.

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Negative LI reflect instability. The higher the absolute value of the negative LI themore unstable is the atmosphere. LI is usually very good correlated to SBCAPE.However, LI has the advantage not to depend on the hight of EL which is usuallya bad estimate in model output.The following thresholds are often applied:

LI ≥ 0K : stable atmosphere - no thunderstorms possible0K > LI ≥ −2K : thunderstorms possible−2K > LI ≥ −6K : thunderstorms likely−6K > LI : severe thunderstorms likely.

(22)

16. Showalter Index - ShowIShowI is defined by Showalter (1947) alike LI but for an air parcel lifted from850hPa rather than the surface. Thresholds are

−3K < ShowI ≤ 3K : thunderstorms possibleShowI ≤ −3K : severe thunderstorms possible.

(23)

17. Deep Convective Index - DCIThe DCI (Barlow, 1993) is a combination of temperature and humidity in 850hPaas well as the LI

DCI = T850 + Td,850 − LI. (24)

Thunderstorms are supposed to be possible if DCI is higher than 30◦C.

18. Thomson Index - ThomIThe Thomson Index is based on the K index and a version of the lifted indexfor the case where not a surface-based air parcel is used but the average over thelowest 50hPa above ground

ThomI = K − LI50hPa. (25)

It should be an improvement of K since it contains information about the layerbelow 850hPa.

19. Theta-E Index TEIThis index provides information about elevated convection. It is the value of thesteepest negative gradient of the equivalent potential temperature Θe, i.e. thelargest cooling and drying with height. If an air parcel is lifted in a layer witha steep cooling and drying it may become warmer than its environment leadingto elevated convection. The condition for this, however, is lifting at the lowerboundary of this layer. Thresholds are

TEI < 5 not favorable5 ≤ TEI < 9 potential

9 ≤ TEI very high potential.(26)

20. Yonetani Index - Y onIThis index is defined by Yonetani and meant to combine conditional instability

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with low-level moisture in order to detect air mass thunderstorms. Yonetani (1979)defined it as

Y onI =

{0.966ΓL + 2.41(ΓU − ΓW ) + 9.66RH − 15 if RH > 0.570.966ΓL + 2.41(ΓU − ΓW ) + 9.66RH − 16.5 if RH ≤ 0.57

(27)

and modified it later (Yonetani, 1990) to

Y onImod =

{0.964ΓL + 2.46(ΓU − ΓW ) + 9.64RH − 13 if RH > 0.570.964ΓL + 2.46(ΓU − ΓW ) + 9.64RH − 14.5 if RH ≤ 0.57.

(28)The variables are

ΓL = lapse rate between 900 and 850hPaΓU = lapse rate between 850 and 500hPaΓW = pseudoadiabatic lapse rate at 850hPaRH = Relative Humidity in [0,1].

(29)

2.3 Wind-related Parameters

1. Vertical Shear - V SVertical shear is the change of wind with height. This change is a vector. Usually,however, only the magnitude is of interest. Many different measures of shear inthe atmosphere exist. Some of them are discussed here.

Higher values of vertical shear usually lead to more organized and persistent thun-derstorms.

(a) Boundary Layer to 6 km Vertical Shear - V SBL−6km

Supercells are usually associated with vertical shear values of 65 to 75kmh .

(b) Effective Bulk Vertical Shear - V SeffThis is the V S within a storm and thus the difference of the wind speedat the LPL and EL. Sometimes only the lowest 40 to 60% of this range isused. Values of 45 to 75km

h and above increase the likelihood of supercells.

(c) Surface-1-km Vertical Shear - V S1

SV1 magnitudes higher than 30kmh tend to favor supercell tornadoes.

(d) Surface-3-km Vertical Shear - V S3

This shear is often used to get a criterion for longevity of convection. Thelarger the shear the longer lasting is the convection. Strong shear also sup-ports high values of helicity. Thresholds are

0− 3 weak4− 5 moderate6− 8 large> 8 severe.

(30)

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(e) Deep Layer Shear - DLSDeep layer shear is defined as the vertical wind shear between the groundlevel (10m) and 6km (usually density weighted in order to approximate massflux). The following thresholds apply

DLS > 40knots : if storms develop then supercellsare likely

40knots ≥ DLS ≥ 30knots : supercells possible if environmentis very unstable

20knots ≥ DLS ≥ 15knots : minimum for organized convectionwith mid level winds of 25 knots.

(31)

2. Storm Relative Winds - SRWStorm relative winds are wind speeds and directions relative to the movementof the storm. The movement of storms can be deducted from radar observationswhile the average environment wind speeds follow from radiosondes or modeloutput. Three kinds of SRW are usually used to a) identify sustained supercells,b) distinguish between tornadic and non-tornadic supercells and c) to classifysupercells into high precipitation, classical and low precipitation.

(a) Surface-2km Storm Relative winds - SRW2

SRW2 is meant to represent low-level storm inflow. The majority ofsustained supercells have values of at least 30km

h .

(b) 4-6-km Storm Relative Winds - SRW4−6

SRW4−6 is used to distinguish between tornadic and non-tornadic supercells.Tornadic supercells have values larger than 30km

h .

(c) Anvil Level/9-11-km Storm Relative Winds - SRWA

SRWA is based on the storm relative wind speeds at anvil height, usuallyapproximated as 9 to 11km They are used to discriminate the precipitationfrom a supercell by

SRA ≤ 40kmh : high precipitation supercell

40kmh < SRA ≤ 110km

h : classic supercell

110kmh < SRA ≥ : low precipitation supercell.

(32)

3. HelicityHelicity is the extent to which corkscrew-like motion occurs. It is generally definedas the following integral over the volume V

H =

∫~u · (∇× ~u)dV. (33)

H is a conservative variable for an incompressible Euler (viscosity free) fluid.

Here we look at the vertical integral of the horizontal wind ~vh and vorticity ~ζhonly. In this case helicity is the vertical integral of the transfer of vorticity from theenvironment into a rising air parcel in convective motion. It is therefore definedas

H =

∫~vh · ~ζh dz =

∫~vh · ∇ × ~vh dz. (34)

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H is zero if the horizontal wind direction does not change with z, since in this case~vh and ∇× ~vh are perpendicular and the scalar product vanishes. H is positive ifthe wind veers (changes clockwise with z) and negative if it backs. The units ofH are m2/s2 = J/kg and thus H is an energy density.

4. Storm Relative Helicity - SRHSRH provides a measure for the wind change with height including its magnitudeand direction in relation to the storm movement. It is introduced by Davies-Joneset al. in 1990. Usually the lowest 3km of the atmosphere are used. It is defined as

SRH = −∫ h

0

~k · (~v(z)− ~c)× ∂~v(z)

∂zdz (35)

with~k = vertical unit vector~c = moving velocity of cell

~v(z) = wind vector.

(36)

SRH is not uniquely calculated since there exist different opportunities to esti-mate ~c from observations. One way to calculate SRH (Markowski and Richardson,2010) is

SRH =N−1∑n=1

[(un+1 − cx)(vn − cy)− (un − cx)(vn+1 − cy)] (37)

with the wind speed components u and v, the components of the cell movingvelocity cx and cy and the height levels n = 1 to N .

Usually one might say that

SRH < 150m2

s2: minor rotation

150m2

s2≤ SRH < 300m2

s2: thunderstorms with rotation

300m2

s2≤ SRH < 450m2

s2: supercells with rotation possible

450m2

s2≤ SRH : supercells with tornadoes possible.

(38)

SRH does not contain any information about the energy of convection. This iswhy the energy helicity index EHI is defined which combines both, SRH andCAPE.

5. Storm Relative Directional Shear SRDSSRDS is a difference of differences. Storm motion has to be estimated first. Thenthe difference between the windspeed at the bottom of convection minus the stormmotion and at 3km altitude minus the storm motion is built. The following thresh-olds apply:

SRDS ≤ 30 : weak30 < SRDS ≤ 60 : some60 < SRDS ≤ 90 : moderate

90 ≤ SRDS : strong

(39)

Strong SRDS is important to produce a favorable environment for tornadoes.

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6. Vorticity Generating Parameter V GPThe vorticity generating parameter is introduced by Rassmussen et al. in 1998 .It is meant as a proxy for the tilting of horizontal vorticity. It is defined as theproduct of the square root of CAPE times the 3-km wind shear, thus

V GP =√CAPE V S3. (40)

Supercell tornadoes are rare if V GP < 0.3 and likely if it is ≤ 0.6.

7. Storm Motion STMThis is the expected speed (vector) with which storms move. Its magnitude isusually estimated as a fraction (e.g. 75%) of the wind speed average of the lowest6km of the atmosphere. Storms move slower than the environmental wind sincethey have higher mass due to the liquid/frozen water content. Vertical wind shearincreases STM . The direction in which the storm moves is usually about 30◦ tothe right of the average wind speed, i.e. the storm veers. This method is sometimescalled 75%30◦ rule. Other values like 80% and 25◦ are also common. However, thisapproach misses any mesoscale dynamics which can lead to large deviations fromreality.

The Bunkers’ method (Bunkers et al., 2000) uses the vector which is 7.5m/s to theright of the bulk shear vector between the 0-500m average wind and the 0-6000maverage wind.

This parameter can be used to estimate also the direction in which tornadoesmove. It is also important in order to calculate the storm relative helicity.

8. Hodograph Length HL

Drawing wind vectors of different altitudes all from the same origin and connectingall tips of the arrows creates a hodograph as a visualization of direction andmagnitude of wind shear with altitude. the length of the hodograph can be usedas a combined index of wind shear direction and magnitude. It does, however, notinclude information of whether the wind is veering or backing with height. HL3is the hodograph length created from wind vectors between 0 and 3 km heightwhile HL6 is build from wind vectors between 0 and 6 km height.

2.4 Advanced Parameters

1. Energy Index - EIDefined by Darkow (1968) EI is the difference of the non-kinetic energy in 500hPaand a certain lower level, usually 850hPa or 925hPa

EI = h500 − h850. (41)

The non-kinetic energy is sometimes also called static energy. For an atmospherewhich does not contain liquid water or ice it is given by

h = cpT + gz + Lvr (42)

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withcp = specific heat of air for constant pressureT = absolute temperature in Kg = earth accelerationz = geopotential heightLv = latent heat of evaporationr = mixing ratio of water vapor.

(43)

Some terms should be altered if there is liquid water and/or ice. The EI is positiveif warm and humid air lays above cold and dry air which is a stable situation. Thefollowing thresholds are applied

EI ≥ 0 No activity expected0 > EI ≥ −2 isolated severe thunderstorms possible−2 > EI severe thunderstorms probable, tornadoes possible.

(44)

Note that the EI only provides a potential for thunderstorms. In case there is astrong CAP which cannot be broken through, nothing might happen.

2. Lifted Condensation Level - LCLThe LCL is the height in which a parcel lifted from the surface becomes saturated.It is therefore a good approximation of the cloud base height in case of forcedascend. LCL is given by

LCL =T2m − Td,2mgcp−

gT 2d,2m

εLvT2m

(45)

with the dew-point temperature Td. In this form LCL is not the absolute heightof the condensation level but the height above ground.

3. Mixed Layer Lifted Condensation Level - LCLML

It is defined as the LCL but not for lifting from the surface but from the mixedlayer (usually approximated by the average over the lowest 100hPa).

4. Level of Free Convection - LFCThe LFC is the height in which a parcel lifted from the surface becomes lighterthan the surrounding air and starts free ascent. In order to calculate it, a par-cel has to be lifted dry-adiabatically from the ground to the LCL and pseudo-adiabatically upwards from the LCL until its density is lower than the density ofthe surrounding air.

The lower the LFC the more likely convection happens. Experience shows thattornadoes seems to be more likely for supercells with LFC less than 2000m aboveground. And thunderstorms are more likely to be initiated and maintained if LFCis below 3000m.

5. Equilibrium Level - EL (Level of Neutral Buoyancy LNB)An air parcel rising adiabatically from the ground beyond its LFC becomes lighterthan the surrounding air and accelerates its ascent. The higher it rises, however,the weaker is the acceleration and at the EL it vanishes. Inertia lets the air parcelrise above the EL, however, with negative buoyancy. EL is primarily used toestimate the height of the anvil of deep convection.

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6. ∆L1 = LFC − LCLThe difference between LFC and LCL contains information about the probabilityof deep convection. If LFC is much higher than LCL chances are good thatconvection stays shallow. If on the other hand the difference between LFC andLCL is small sudden deep convection can occur.

7. ∆L2 = EL− LFCThe difference between EL and LFC provides a measure of deepness of convectionif convection occurs.

8. Convective Available Potential Energy - CAPEDifferent types of CAPE are defined for different purposes. They all have incommon that they are a measure of energy available for convection in case ofno entrainment and thus are the integral over buoyancy. The major variablestherefore are the virtual potential temperatures of an air parcel Θv,p and of theenvironmental air Θv,e. Usually the following thresholds apply for CAPE

0 Jkg < CAPE ≤ 1000 J

kg : weak instability

1000 Jkg < CAPE ≤ 2500 J

kg : moderate instability

2500 Jkg < CAPE ≤ 4000 J

kg : strong instability

4000 Jkg < CAPE : extreme instability.

(46)

(a) Surface Based CAPE - SBCAPESBCAPE is defined as the integral

SBCAPE = g

∫ EL

LFC

Θv,p −Θv,e

Θv,edz. (47)

It is the energy that is available for convection of an air parcel that is liftedfrom the surface to its LFC.

(b) Normalized CAPE - NCAPENCAPE is an energy density of a vertical column. Since the energy releasedescribed by SBCAPE happens between the LFC and EL, NCAPE isdefined as

NCAPE =SBCAPE

EL− LFC. (48)

NCAPE is therefore a measure of acceleration (mass specific energy dividedby length). High values of NCAPE represent fast development.

(c) Mixed Layer CAPE - MLCAPEMLCAPE uses not only parcels rising from ground level but from thewhole mixed layer which is usually approximated as the lowest approximately100mb layer. Different approximations for MLCAPE are used. Usually the

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following thresholds apply

0 Jkg < MLCAPE ≤ 1000 J

kg : weak instability

1000 Jkg < MLCAPE ≤ 2500 J

kg : moderate instability

2500 Jkg < MLCAPE ≤ 3500 J

kg : strong instability

3500 Jkg < MLCAPE : extreme instability

(49)

(d) Maximum Unstable CAPE - MUCAPEMUCAPE is the CAPE of the most unstable parcel within the lowest300hPa. Note that each parcel has its own LCL, LFC and EL.

(e) 3kmCAPE3kmCAPE characterizes the CAPE of the lowest 3km and is defined as

3kmCAPE =

gmin(EL,3km)∫

LFC

Θv,p−Θv,e

Θv,edz if LFC < 3km

0 if LFC > 3km or no LFC(50)

High values of 3kmCAPE indicate high accelerations in low layers. Convec-tion is more likely to start explosively in this case.

(f) Integrated CAPEIntegrated CAPE ore (ICAPE) is a column specific variable rather than amass specific one. Thus it is provided in J/m2 instead of J/kg. ICAPE canbe defined as the sum over CAPE ·dp/g along the column. It seems thatthere is not much experience with this variable which is defined by Mapes(1993).

9. Convective Inhibition - CINCIN is the energy needed to lift an air parcel from the surface to its LFC

CIN = g

LFC∫0

Θv,p −Θv,e

Θv,edz. (51)

If CIN is very low or if there is no CIN at all, convection starts in an earlystate of instability and only minor convection may happen. If it is too strong,then it cannot be overcome and no thunderstorms can be triggered except in caseof forced lifting e.g. by mountains or large-scale dynamic forcing like confluence.The following thresholds usually apply:

CIN ≤ 15 Jkg : only minor cumuli develop

15 Jkg < CIN ≤ 50 J

kg : single cell thunderstorms possible

50 Jkg < CIN ≤ 200 J

kg : multi cell thunderstorms possible

200 Jkg < CIN : stability of stratification too high to overcome

no thunderstorms develop.(52)

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10. Upward Vertical Velocity UV VThe upward vertical velocity represents the maximum vertical wind speed. Ac-cording to parcel theory it is defined as

UV V =√

2CAPE. (53)

The following thresholds in m/s are used:

UV V ≤ 40 : regular updraft40 < UV V ≤ 60 : strong updraft60 < UV V ≤ 80 : very strong updraft

81 < UV V : extreme updraft.

(54)

Real updraft should be slower due to water and ice in the air and entrainment.Thus, the higher the water content the lower is w compared to UV V . Wind shearenables updrafts to persist longer. Rotating cells can have considerably largerupdraft speeds. The potential of hail increases which increasing UV V . Large hailrequires very strong to extreme updraft pertained by wind shear.

11. Lifted Parcel Level - LPLThis is the height of the most unstable air parcel used in MUCAPE. It allows toidentify the layer with highest CAPE.

12. Liquid Water Content - LWCHigh liquid water content is a product of strong condensation which releasedhigh amounts of energy. On the other hand, if liquid water falls into layers withrelative humidity below 100% the water starts evaporating and by that coolingits environment. This leads to negative buoyancy and finally to downdraft. Thusthe liquid water content can be used for the estimation of downdraft probabilityand strength.

13. Wet Bulb Zero Level - WBZThis is the height in which the wet bulb temperature is zero, sometimes also calledWB0. Furthermore the name freezing level FRZ is used occasionally. WBZ is animportant parameter with respect to hail and downdrafts since hail starts meltingat that altitude and that melting cools the air. The higher the WBZ the less likelyhail reaches the ground but the more likely downdrafts occur. The cooling itselflowers the WBZ).

14. Water Vapor Convergence - WV CThis parameter describes the water vapor convergence in the lower troposphere.It is defined as

WV C = −p∫

p0

∇ · (q ~vh)dp

g(55)

with p0 = 925hPa and p = 700hPa if orography is higher than 550m and p0 =1000hPa and p = 850hPa otherwise. q is the specific humidity. A threshold forconvection due to water vapor convergence is 0.1 · 10−4gm2/s.

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15. Craven Parameter CThe Craven Parameter C is the simple product of 100mb MLCAPE and thedeep layer shear (0 − 6km, magnitude of the vector difference). The majority ofsignificant severe events (hail (d > 5cm), winds (v > 120km/h), tornadoes ≥ F2)occur when the product exceeds 20, 000m3/s3. Some authors say that extremeevents are likely if it exceeds 10, 000m3/s3

The index is formulated as follows:

C = MLCAPE[J/kg] · DLS[m/s] (56)

16. Energy Helicity Index - EHIEHI is defined by Hart and Korotky (1991) as the normalized product of stormrelative helicity and CAPE

EHI =CAPE · SRH

160, 000. (57)

It therefore combines a measure of static instability with dynamics. It is a usefulestimate of tornado risk with the following thresholds:

EHI > 1 : Potential for supercells5 ≥ EHI > 1 : up to F3 tornadoes possible

EHI > 5 : up to F5 tornadoes possible.(58)

Note that tornadoes are also possible if EHI is small due to small CAPE as longas SRH is high. Furthermore a sounding may not be representative since helicitymay have high spatial variability.

17. Stability and Wind Shear Index for thunderstorms in Switzerland - SWISSTwo indices are developed in Switzerland (Huntrieser et al., 1997) in order toforecast thunderstorm possibility based on 00UTC and 12UTC observations:

(a) SWISS00

SWISS00 = ShowI + 0.4V S3−6km + 0.1(T600 − Td,600) (59)

where V S3−6km is the vertical wind shear between 3km and 6km aboveground.

(b) SWISS12

SWISS12 = LI − 0.1V S0−3km + 0.1(T650 − Td,650) (60)

where V S0−3km is the vertical wind shear between 10m and 3km aboveground.

18. Enhanced Stretching Potential - ESPESP is developed by Jon Davies (2005) as a guidline for the development of non-supercell/nonmesocyclone tornadoes. It is thus a useful tool in environments withsmall SRH and high LCL. The tornadoes that develop under these conditions are

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usually weak (F0-F1) but can be strong (F2-F3) occasionally. ESP is computedas

ESP =

{ ∣∣∣(γ0−2km − 7◦C) min(MLCAPE3km,100J/kg)50J/kg

∣∣∣ if SBCAPE ≥ 500J/kg

0 else.(61)

According to Jon Davies, who did not publish this index, it should be used withcare. However, in cases of lines of strong wind shift boundaries, non-supercelltornadoes may occur. And this is in line with high values of the ESP .

19. Bulk Richardson Number - BRNThe Bulk Richardson Number is defined by Weisman and Klemp (1982) as theratio of CAPE to the squared wind shear

BRN =CAPE

0.5(v1 − v2)2. (62)

v1 and v2 are wind speeds in different levels, usually 500m and 6km. BRN isusually used to distinguish different kinds of thunderstorms:

BRN < 10 : thunderstorms unlikely10 ≤ BRN < 45 : supercells possible45 ≤ BRN : single cells and multi cells possible

(63)

Since this index is a ratio of two energies it should always be interpreted togetherwith the absolute values of the energies. CAPE characterizes vertical instabilitywhile the wind shear tells more about the character of storms. Low wind shearmakes multi-cells unlikely and single pulses likely, if enough CAPE is available.Directional wind shear counteracts multi-cell development while speed shear sup-ports it. Supercells are most likely when BRN is in its tens.

20. Dynamic State Index - DSIThis very interesting index is developed by Peter Nevir from Freie UniversitatBerlin. It measures the distance from hydrostatic and geostrophic equilibrium. Ihad no time to include it here.

21. Divergence of Q VectorThe divergence of the Q vector is sometimes used as a measure of instability.

2.5 Thematic Parameters

1. Severe Weather Threat Index SWEATSWEAT is defined by Miller (1972). It consists of four terms

SWEAT = a+ b+ c+ d (64)

with the humidity terma = 12Td850 (65)

the instability term

b = 20

{(TT − 49) if TT > 49◦C0 else

(66)

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the shear termc = 2v850 − v500 (67)

where the wind speeds have to be provided in knots. The last term is a veeringterm in case there is veering

d =

{125 (sin(dd500 − dd850) + 0.2) if dd500 − dd850 > 00 else

). (68)

ddp means the wind direction in hight level p. dd500−dd850 is the veering between500hPa and 850hPa. If the wind direction in 500hPa is 200◦ and in 850hPa is220◦ the difference is −20◦ and thus the wind is not veering. Further conditionsthat are applied by some authors are

210◦ ≤ dd500 ≤ 310◦

130◦ ≤ dd850 ≤ 250◦

d500 > d850

v500 > 15knots ≈ 28kmh

v850 > 15knots ≈ 28kmh

(69)

With the last term the SWEAT includes dynamical effects. Veering in 850 to500hPa suggests warm air advection which due to the omega equation impliesupward motion. The following thresholds apply:

150 < SWEAT ≤ 300 : Slight severe300 < SWEAT ≤ 400 : Severe possible

400 < SWEAT : Tornadic possible.(70)

2. Downdraft CAPE - DCAPEDCAPE characterizes the available potential energy of downdraft. The integralis from the surface to the level of free sink LFS

DCAPE = g

∫ LFS

0

Θv,p −Θv,e

Θv,edz (71)

Θv,p is usually approximated by the wet bulb potential temperature Θw of thesinking parcel, which is the temperature it achieves if rain water or ice is evap-orated. The LFS is usually approximated as the height in which the wet bulbtemperature is zero (WBZ). The square root of 2 ·DCAPE is the gain in down-draft velocity from LFS to the ground due to evaporation within the descendingair parcel in case of no entrainment and detrainment of air.

3. Supercell Composite Parameter - SCPSCP combines CAPE, SRH and V S as

SCP =MUCAPE

1000J/kg

SRH0−3km

100m2/s2

DLS2

40m2/s2(72)

Usually values greater than 1 strongly favor supercells, while non-supercell stormsare generally associated with SCP values less than 1. A detailed discussion canbe found at Thompson et al. (2003).They found Mean SCP values of 4 in case ofsupercells and 0.2 in case of nonsupercells.

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4. Significant Tornado Parameter - STPOne definition of STP is

STP =DLS

20m/s

SRH0−1km

100m2/s2

MLCAPE

1000J/kg

2000− LCLML

1500m(73)

while NOAA provides

STP =DLS

20m/s

SRH0−1km

100m2/s2

SBCAPE

1500J/kg

2000− LCLSB

1500m

100 + SBCIN

150J/kg(74)

with the conditions that

• the LCLSB term is set to 1 if LCLSB is less than 1000m,

• the SBCIN term is set to 1 if SBCIN > −50J/kg, and

• the DLS term is capped at 1.5 and set to zero if DLS < 12.5m/s.

A majority of significant tornadoes (F2 and larger damage) have been associatedwith STP > 1 while the most non-tornadic supercells have been associated withSTP < 1.

5. Significant Hail Parameter - SHIPAccording to NOAA this parameter is designed to distinguish between significanthail ( with diameters ≥ 2cm and non-significant hail. It is based on 5 parametersand given as

SHIP =−MUCAPE qMU γ500−700hPa T500hPaDLS

44 · 10−6(75)

with

qMU = water vapor mixing ratio of MU parcel in g/kgγ500−700hPa = 700-500hPa lapse rate in ◦C/km

DLS = Deep Layer Shear in m/s.(76)

SHIP values greater than 1 indicate a favorable environment for significant hail.Values larger than 4 are considered very high. Values larger than 1.5 to 2 areusually linked to observed significant hail.

6. Lightning Potential Index LPIThe LPI is designed by NOAA as an empirical estimate of lightning risk. It isdefined as

LPI = (A+B) · (T850 − 272K) (77)

limited between 0 and 20000 and with the parameters

A = −RH2 ·(

dΘedz

∣∣∣600hPa

)2(min(LI, 0))2

B = 0.001 ·muCAPE · PW ·RH(78)

with the relative humidity RH, the equivalent potential temperature lapse ratedΘedz in 600hPa, the lifted index LI, the precipitable water PW , and the maximum

unstable CAPE muCAPE of the lowest 3000m above ground. The temperaturein 850hPa has to be provided in Kelvin. 272K are subtracted in order to allowthunderstorms with lightning only in case of temperatures at 850hPa larger than-1.15 degrees Celsius. Further lightning indices exist which are not discussed here.

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7. Supercell Detection Index - SDIThe supercell detection index SDI is meant to be applied to high resolutionmodels. It is introduced on the basis of Doswell and Burgess (1993) by Droegemeieret al. (1993). Two variables are considered: vertical relative vorticity ζ and verticalwind speed w. These variables need to be available on a fine spatial grid (e.g. 2kmhorizontal resolution). Then for each location an environment is defined, say 10grid points in each direction. They are used to define averages of ζ and w. Knowingthe environmental average for each grid point allows for the estimation of the localdeviation from the average and thus the estimation of the local correlation betweenζ and w. The SDI is defined by this correlation multiplied by the column averageof ζ (ζ) at the location as

SDI =〈w′ζ ′〉(

〈w′〉2 〈ζ ′〉)0.5 · ζ. (79)

Values of SDI = 3 · 10−4s−1 are a minimum for the development of supercells.The SDI can be seen as a proxy of helicity.

8. Derecho Composite Parameter DCPThe DCP takes four pieces of information into account: 1. the development of asufficient cold pool by means of DCAPE, 2. the degree of organization by windshear, 3. the mean wind speed to allow downstream development, and 4. the abilityto sustain strong storms at the leading edge by means of MUCAPE. Evans andDoswell (2001, [?]) proposed the following formula

DCP =DCAPE

890 Jkg

Shear0−6km

20kts

MeanWind0−6km

16kts

MUCAPE

2000 Jkg

. (80)

I calculated DCP for some days on which derechoes occurred in Germany basedon data provided by Christoph Gatzen and got no meaningful results. It seamsthat this parameter is so much tailored to conditions in the US that it can hardlybe used in Europe.

9. Conditional Probability of MCS maintenance MMPMike Coniglio (NSSL) suggested this parameter. As a probability it can take valuesbetween 0 and 1. He proposed the following formula from a fit to observations

MMP = 1/ {1 + exp [a0 + a1ms+ a2 lr + a3MUCAPE + a4mw]} (81)

with a0 = 13, a1 = −4.59 · 10−2, a2 = −1.16, a3 = −6.17 · 10−4, and a4 = −0.17.The variables are

ms = maximum bulk shear between 0-1km and 6-10km above ground [m/s]lr = lapse rate in 3 to 8 km in K/km

MUCAPE = most unstable CAPE in J/kgmw = mean wind speed in 3 to 12 km.

(82)MMP is set to zero for MUCAPE < 100J/kg. This parameter has the distinctadvantage that it is given as a probability and therefore easy to interpret.

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10. Conditional Probability of MCS forward speed > 18 m/s MSPAlso developed by Mike Coniglio (NSSL) this parameter estimates the likelihoodthat MCS get a forward speed above 18m/s. MCS with forward speeds abovethis threshold are much more likely to produce widespread damage than thosemoving slower. The parameter is calculated with respect to some standardizedvalues. It is defined as

MSP = 1/ {1 + exp [a0 + a1 dθxz + a2mw + a3 lrz]} (83)

with a0 = −3.46, a1 = 0.447, a2 = 0.1119, a3 = 0.79 and

dθxz = standardized values of max. diff. in θe between low and mid levelsmw = 2− 12km mean wind speed in m/slrz = standardized values of 2-6km lapse rate.

(84)The standardization is to be done with the local history of the respective param-eters.

MSP is set to zero for MUCAPE < 100J/kg.

References

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[10] Doswell, C.A. III, D.W. Burgess, 1993: Tornadoes and tornadic storms: A review ofconceptual models. The Tornado: Its Structure, Dynamics, Prediction, and Hazards(Church et al., eds.) Amer. Geophys. Union, Geophys. Monogr. 79, 161-172.

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[26] Thompson, R.L., R. Edwards, J.A. Hart, K.L. Elmore, and P. Markowski, 2003:Close procimity soundings within supercell envrinments obtained from the RapidUpdate Cycle. Wea. Forecasting, 18 , 1243-1261.

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